D. Arzelier, D. Peaucelle, E. Prempain, J. Camino, J. Swevers
This note aims at providing some background and comments to the paper by M. Durrant, H. Werner and K. Abbott published in this issue. This paper proposes a comparison between the so-called GloverMcFarlane loop shaping design procedure (LSDP) and the Lyapunov-based design procedure (called ellisoidal set formulation) proposed in [25]. The synthesis procedures are evaluated via the design of robust multi-performance reduced-order controllers for a voltage source converter high voltage direct current (VSC HVDC) power plant terminal that is operating over different points. The present discussion will focus on the theoretical problem of the synthesis of robust multi-performance reduced-order controllers for linear uncertain models rather than on the practical control problem. It is well-known that this particular control problem is extremely difficult [1]. Even the simplified problem of reduced-order controller synthesis for a given plant is still an open problem. The present problem has been extensively studied and the format of a discussion section in European Journal of Control is clearly too stringent to include all the possible references. Therefore, the objective of this note is not to give a complete and fair evaluation of the existing methods in a very rich literature but rather to give some brief comments and additional references to the interested reader. First, we would like to comment two issues with respect to the ellipsoidal set formulation. When comparing with other formulations, this parameterization has the advantage to allow multiobjective or multi-operating points design without the conservative constraints introduced by the Lyapunov shaping paradigm (LSP) [23]. Yet, this property may be used in a richer way than it is here in [8]. Indeed, the multi-objective problems may also have inhomogeneous dimensions. In particular, the specifications may be defined for models of different orders. This is often the case when including weighting functions in the design process. Another debatable point may be raised about the application of the convexifying approach to this particular formulation. Indeed, it seems that the converging point of the algorithm is located on the boundaries of the nonlinear nonconvex inequality constraint leading to the loss of the main characteristic of the proposed parameterization: convex sets (ellipsoids) of controllers. This property has been used in [25] to choose the best controllers in the set with respect to resilience properties. We have some doubts about the effectiveness of this resilience procedure when using the convexifying approach. This last remark naturally leads to the discussion about numerical issues. The control problem encountered in the present paper may be recast as the following nonconvex nonlinear optimization problem:
本说明旨在为M. Durrant, H. Werner和K. Abbott在本期发表的论文提供一些背景和评论。本文提出了所谓的GloverMcFarlane回路成形设计程序(LSDP)与b[25]中提出的基于lyapunov的设计程序(称为ellisoidal set公式化)的比较。针对运行在不同点上的电压源变换器高压直流(VSC HVDC)电厂终端，通过设计鲁棒多性能降阶控制器来评估综合过程。本文将重点讨论线性不确定模型的鲁棒多性能降阶控制器的综合理论问题，而不是实际控制问题。众所周知，这个特殊的控制问题是极其困难的。即使是给定对象的降阶控制器综合的简化问题，仍然是一个开放的问题。目前的问题已被广泛研究，《欧洲控制杂志》讨论部分的格式显然过于严格，无法包括所有可能的参考文献。因此，本说明的目的不是在非常丰富的文献中对现有方法进行完整和公平的评价，而是为感兴趣的读者提供一些简短的评论和额外的参考资料。首先，我们想评论关于椭球集公式的两个问题。与其他公式相比，这种参数化的优点是允许多目标或多工作点设计，而不需要Lyapunov成形范式(LSP)[23]引入的保守约束。然而，这个属性可以以比[8]更丰富的方式使用。事实上，多目标问题也可能具有非齐次维度。具体来说，可以为不同订单的型号定义规格。当在设计过程中包含权重函数时，通常会出现这种情况。关于将凸化方法应用于这个特殊公式，可能会提出另一个有争议的问题。实际上，该算法的收敛点似乎位于非线性非凸不等式约束的边界上，导致所提出的参数化的主要特征:控制器的凸集(椭球)丢失。这个属性在[25]中被用来根据弹性属性选择集合中最好的控制器。当使用凸化方法时，我们对这种弹性过程的有效性存在一些怀疑。最后这句话很自然地引出了关于数字问题的讨论。本文中遇到的控制问题可以重新刻写为以下的非凸非线性优化问题:
{"title":"Discussion on: \"Design of Low Order Robust Controllers for a VSC HVDC Power Plant Terminal\"","authors":"D. Arzelier, D. Peaucelle, E. Prempain, J. Camino, J. Swevers","doi":"10.3166/ejc.13.552-557","DOIUrl":"https://doi.org/10.3166/ejc.13.552-557","url":null,"abstract":"This note aims at providing some background and comments to the paper by M. Durrant, H. Werner and K. Abbott published in this issue. This paper proposes a comparison between the so-called GloverMcFarlane loop shaping design procedure (LSDP) and the Lyapunov-based design procedure (called ellisoidal set formulation) proposed in [25]. The synthesis procedures are evaluated via the design of robust multi-performance reduced-order controllers for a voltage source converter high voltage direct current (VSC HVDC) power plant terminal that is operating over different points. The present discussion will focus on the theoretical problem of the synthesis of robust multi-performance reduced-order controllers for linear uncertain models rather than on the practical control problem. It is well-known that this particular control problem is extremely difficult [1]. Even the simplified problem of reduced-order controller synthesis for a given plant is still an open problem. The present problem has been extensively studied and the format of a discussion section in European Journal of Control is clearly too stringent to include all the possible references. Therefore, the objective of this note is not to give a complete and fair evaluation of the existing methods in a very rich literature but rather to give some brief comments and additional references to the interested reader. First, we would like to comment two issues with respect to the ellipsoidal set formulation. When comparing with other formulations, this parameterization has the advantage to allow multiobjective or multi-operating points design without the conservative constraints introduced by the Lyapunov shaping paradigm (LSP) [23]. Yet, this property may be used in a richer way than it is here in [8]. Indeed, the multi-objective problems may also have inhomogeneous dimensions. In particular, the specifications may be defined for models of different orders. This is often the case when including weighting functions in the design process. Another debatable point may be raised about the application of the convexifying approach to this particular formulation. Indeed, it seems that the converging point of the algorithm is located on the boundaries of the nonlinear nonconvex inequality constraint leading to the loss of the main characteristic of the proposed parameterization: convex sets (ellipsoids) of controllers. This property has been used in [25] to choose the best controllers in the set with respect to resilience properties. We have some doubts about the effectiveness of this resilience procedure when using the convexifying approach. This last remark naturally leads to the discussion about numerical issues. The control problem encountered in the present paper may be recast as the following nonconvex nonlinear optimization problem:","PeriodicalId":11813,"journal":{"name":"Eur. J. Control","volume":"171 1","pages":"552-557"},"PeriodicalIF":0.0,"publicationDate":"2007-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74134930","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
J. VanAntwerp, R. Braatz, T. Alamo, D. M. D. L. Peña, I. Alvarado, D. Limón
{"title":"Discussion on: \"GPC Robust Design Using Linear and/or Bilinear Matrix Inequalities\"","authors":"J. VanAntwerp, R. Braatz, T. Alamo, D. M. D. L. Peña, I. Alvarado, D. Limón","doi":"10.3166/ejc.13.468-472","DOIUrl":"https://doi.org/10.3166/ejc.13.468-472","url":null,"abstract":"","PeriodicalId":11813,"journal":{"name":"Eur. J. Control","volume":"97 1","pages":"468-472"},"PeriodicalIF":0.0,"publicationDate":"2007-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74827425","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Discussion on: \"Backstepping Controller Design Using Neural Networks for a Fighter Aircraft\"","authors":"R. Sattigeri, A. Calise, Byoung-Soo Kim","doi":"10.3166/ejc.13.527-528","DOIUrl":"https://doi.org/10.3166/ejc.13.527-528","url":null,"abstract":"","PeriodicalId":11813,"journal":{"name":"Eur. J. Control","volume":"15 1","pages":"527-528"},"PeriodicalIF":0.0,"publicationDate":"2007-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74577874","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
K. Macek, J. Matuško, Agostino Martinelli, R. Siegwart, Jose Alfredo Guerrero Mata, R. Lozano
{"title":"Discussion on: \"Adaptive and Predictive Path Tracking Control for Off-road Mobile Robots\"","authors":"K. Macek, J. Matuško, Agostino Martinelli, R. Siegwart, Jose Alfredo Guerrero Mata, R. Lozano","doi":"10.3166/ejc.13.440-446","DOIUrl":"https://doi.org/10.3166/ejc.13.440-446","url":null,"abstract":"","PeriodicalId":11813,"journal":{"name":"Eur. J. Control","volume":"38 1","pages":"440-446"},"PeriodicalIF":0.0,"publicationDate":"2007-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85291367","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Discussion on: ''Symmetry Reduction and Control of the Dynamics of a 2-D Rigid Circular Cylinder and a Point Vortex: Vortex Capture and Scattering''","authors":"Sebastián J. Ferraro, D. D. Diego","doi":"10.3166/ejc.13.656-658","DOIUrl":"https://doi.org/10.3166/ejc.13.656-658","url":null,"abstract":"","PeriodicalId":11813,"journal":{"name":"Eur. J. Control","volume":"70 1","pages":"656-658"},"PeriodicalIF":0.0,"publicationDate":"2007-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89417717","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Discussion on: \"Mean Square Exponential Stability for Stochastic Linear Discrete Time Systems\"","authors":"H. Chizeck, Chun-I Chen, Y. Ji","doi":"10.3166/ejc.12.396-399","DOIUrl":"https://doi.org/10.3166/ejc.12.396-399","url":null,"abstract":"","PeriodicalId":11813,"journal":{"name":"Eur. J. Control","volume":"147 1","pages":"396-399"},"PeriodicalIF":0.0,"publicationDate":"2006-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77703353","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In the paper under discussion, the authors consider the problem of designing switching controllers for plants that are subject to large levels of uncertainty or to abrupt changes in their dynamics. There has been a great deal of interest in this problem in the recent past [7,2], and the potential applications of switching controllers are numerous. For instance, one approach to the design of fault-tolerant systems [3,4] is to construct models and controllers for the various operating conditions corresponding to different system malfunctions. Once the correct plant has been identified, the associated controller is switched on. Of course, in order for this type of scheme to be practical, it is vitally important to be able to identify the correct plant as quickly and efficiently as possible, and tominimise any transient effects which may result from switching to incorrect controllers during the identification process. A major issue in the design of switching control schemes is that the system can switch to destabilising controllers before finally locking onto the correct one, which leads to very poor transient behaviour. We shall refer to such switches as destabilising switches throughout this discussion. The primary contribution of the paper is to describe a novel switching control scheme, which reduces the number of undesirable, destabilising switches that occur while identifying the correct plant. In fact, under a range of assumptions, which we shall discuss in detail below, the correct plant can be identified after a finite number of switches, at most one of which is destabilising. The authors also give an upper bound on the number of switches required in order to find the correct plant. The architecture underpinning the MLSC scheme consists of several layers or levels of controllers. In fact, given n plants, P1, . . . ,Pn, the proposed architecture consists of n 2 layers, each of which contains a number of controllers. The various control layers are constructed in such a way that if i denotes the layer number, C and C0 denote controllers, and P denotes a plant model, then:
{"title":"Discussion on: \"Multi-layer Switching Control using Generalized Sampled-data Hold Functions\"","authors":"M. Verwoerd, O. Mason","doi":"10.3166/ejc.12.500-504","DOIUrl":"https://doi.org/10.3166/ejc.12.500-504","url":null,"abstract":"In the paper under discussion, the authors consider the problem of designing switching controllers for plants that are subject to large levels of uncertainty or to abrupt changes in their dynamics. There has been a great deal of interest in this problem in the recent past [7,2], and the potential applications of switching controllers are numerous. For instance, one approach to the design of fault-tolerant systems [3,4] is to construct models and controllers for the various operating conditions corresponding to different system malfunctions. Once the correct plant has been identified, the associated controller is switched on. Of course, in order for this type of scheme to be practical, it is vitally important to be able to identify the correct plant as quickly and efficiently as possible, and tominimise any transient effects which may result from switching to incorrect controllers during the identification process. A major issue in the design of switching control schemes is that the system can switch to destabilising controllers before finally locking onto the correct one, which leads to very poor transient behaviour. We shall refer to such switches as destabilising switches throughout this discussion. The primary contribution of the paper is to describe a novel switching control scheme, which reduces the number of undesirable, destabilising switches that occur while identifying the correct plant. In fact, under a range of assumptions, which we shall discuss in detail below, the correct plant can be identified after a finite number of switches, at most one of which is destabilising. The authors also give an upper bound on the number of switches required in order to find the correct plant. The architecture underpinning the MLSC scheme consists of several layers or levels of controllers. In fact, given n plants, P1, . . . ,Pn, the proposed architecture consists of n 2 layers, each of which contains a number of controllers. The various control layers are constructed in such a way that if i denotes the layer number, C and C0 denote controllers, and P denotes a plant model, then:","PeriodicalId":11813,"journal":{"name":"Eur. J. Control","volume":"21 1","pages":"500-504"},"PeriodicalIF":0.0,"publicationDate":"2006-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73957853","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
where x(t) ∈ IR is the state, u(t) ∈ IR is the known input, v(t) ∈ IR is the unknown input, which can be considered as the effect of the actuator failure, and y(t) ∈ IR is the measurement output. Without loss of generality, we have rank D = q and rankC = p. The problem of the state estimation in this case is the well known unknown input one, see [4] and the references given in [2]. The necessary and sufficient conditions for the existence and the stability of the full order or reduced order observers are
{"title":"Discussion on: A Comparison of Sliding Mode and Unknown Input Observer for Fault Reconstruction","authors":"M. Darouach, M. Zasadzinski, L. Boutat-Baddas","doi":"10.3166/ejc.12.261-277","DOIUrl":"https://doi.org/10.3166/ejc.12.261-277","url":null,"abstract":"where x(t) ∈ IR is the state, u(t) ∈ IR is the known input, v(t) ∈ IR is the unknown input, which can be considered as the effect of the actuator failure, and y(t) ∈ IR is the measurement output. Without loss of generality, we have rank D = q and rankC = p. The problem of the state estimation in this case is the well known unknown input one, see [4] and the references given in [2]. The necessary and sufficient conditions for the existence and the stability of the full order or reduced order observers are","PeriodicalId":11813,"journal":{"name":"Eur. J. Control","volume":"10 1","pages":"261-277"},"PeriodicalIF":0.0,"publicationDate":"2006-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83959753","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Discussion on: \"Energy-to-Peak Model Reduction for 2-D Discrete Systems in Fornasini-Marchesini Form\"","authors":"O. Kaneko","doi":"10.3166/ejc.12.431-436","DOIUrl":"https://doi.org/10.3166/ejc.12.431-436","url":null,"abstract":"","PeriodicalId":11813,"journal":{"name":"Eur. J. Control","volume":"39 1","pages":"431-436"},"PeriodicalIF":0.0,"publicationDate":"2006-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90252840","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Discussion on: \"Application of Logarithmic-based Parameter and Upper Bounding Estimation Rules to Adaptive-Robust Control of Robot Manipulators\"","authors":"E. Yaz","doi":"10.3166/ejc.12.171-175","DOIUrl":"https://doi.org/10.3166/ejc.12.171-175","url":null,"abstract":"","PeriodicalId":11813,"journal":{"name":"Eur. J. Control","volume":"43 1","pages":"171-175"},"PeriodicalIF":0.0,"publicationDate":"2006-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82877111","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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